A division-of-focal-plane polarimeter based on a dichroic dye and liquid crystal polymer guest-host system is presented. Two Stokes polarimeters are demonstrated: a linear Stokes and the first ever Full-Stokes division-of-focal-plane polarimeter. The fabrication, packaging, and characterization of the systems are presented. Finally, optimized polarimeter designs are discussed for future works.
©2012 Optical Society of America
The primary attributes of an optical field are its intensity, wavelength, coherence and polarization. An imaging polarimeter is a camera that samples the polarization state across a scene. There is a wide variety of applications for imaging polarimeters, including, remote sensing , medical imaging [2, 3], and interferometry [4, 5]. A polarimeter functions by recording multiple pixelated intensity measurements through varying polarization filters. In a simple configuration these polarization filters can consist of a 0°, 45°, 90°, and 135° linear and right- and left-handed circular polarizers. A Stokes imaging polarimeter then uses the measurements to estimate the incident polarization state, which can be quantified as a Stokes vector. A Stokes vector, , consists of four elements S0, S1, S2, and S3, which can be defined using the set of intensity measurements mentioned previously,
Here S1 and S2 represent the affinity towards linear polarization. S3 denotes the fraction of the intensity that is circularly polarized. While S0 must be greater than zero, S1,2,3 can range zero to ± S0. Important metrics that can be calculated from a Stokes vector are the angle of linear polarization, degree of polarization (DOP), degree of linear polarization (DOLP), and degree of circular polarization (DOCP), shown in Eqs. (2)–(5) respectively .
An imaging polarimeter is not limited to measuring the intensities referenced in Eq. (1). The instrument must capture a minimum of four measurements to calculate the complete vector and must include at least one measurement that is not coplanar with the others when plotted on the Poincaré Sphere. A wide variety of imaging polarimeter configurations exist, but almost all of them can be categorized as either a division of time (DoTP), amplitude (DoAmP), aperture (DoAP), or focal-plane (DoFP) polarimeter. An overview of the different configurations is given by Tyo, et al. . A DoFP Stokes imaging polarimeter uses a polarization focal plane array (FPA) that is analogous to a Bayer color filter FPA  in that neighboring pixels on an image sensor have varying filters. Most often the FPA pattern consists of an array of 0°, 45°, 90°, and 135° linear polarizers, as shown in Fig. 1(a) . Figure 1(b) illustrates how each pixel in a macro pixel detects a separate linear polarization orientation using a linear polarizer mounted directly above a pixel in an image sensor. These four intensity measurements are used to estimate the incident polarization. This configuration is only capable of measuring the linear components of the Stokes vector, S1 and S2. A circular polarization measurement requires an elliptical or circular polarizer to be included in the system. Thus far the vast majority of DoFP polarimeters are based on wire-grid polarizer arrays which can be fabricated on a separate substrate  or directly on the sensor , however, patterned polyvinyl-alcohol (PVA) polarizers  and birefringent crystals have also been used . In this paper we demonstrate the use of patterned liquid crystal polymer (LCP) polarizers and retarders to construct both a linear and a full Stokes DoFP imaging polarimeter. Previously we demonstrated the fabrication of patterned LCP polarizers as small as 3 μm  and retarders as small as 4 μm . Performance of and polarization images from the two liquid crystal polymer based polarimeters are presented. This paper follows the methodology given by both Tyo et al , LaCasse et al , and Chipman . A brief overview is given in Appendix A.
2. Focal plane array polarization filter fabrication
Patterned LCP films are fabricated using a linearly photopolymerizable polymer (LPP) photoalignment material, which anisotropically cross-links when exposed to linearly polarized ultraviolet (LPUV) light [17, 18]. This material is used as a patternable substitute for mechanically buffed substrates. The alignment orientation is defined by exposing the material to linearly polarized ultraviolet light (LPUV) and therefore patterned alignment domains can be defined using traditional photolithography techniques with the addition of a linear polarizer. The photoalignment material is model LIA-01 by Dainippon Ink and Chemical. The LCP is model RMS08 manufactured by EMD Chemicals and is a dry powder that is added to a solvent before coating. Dichroic dye is added to the LCP/solvent mixture to add absorption to the material. The dyes used are models G-241 and G-472, which have peak absorption at 553 nm and 619 nm respectively and are produced by Hayashibara Biochemical Laboratories, Inc. The substrates used are 100 mm diameter 0.5 mm thick borosilicate double side polished wafers.
The DoFP polarimeter is designed around the monochromatic Kodak KAI-2020 CCD. This CCD array is comprised of a 1600x1200 active pixel array where each pixel is 7.4 μm square.
Accurate alignment marks are crucial for defining the unique polarization domains in the photoalignment material (PM) layer. Therefore they must first be deposited or etched onto the glass. Both etching of the glass using hydrogen fluoride and electron beam deposition of chrome were explored, however it was found the etched glass lacked adequate contrast during dicing of the finished wafers. The chrome was patterned with a standard lift-off process and a total of 50 nm was deposited. Figure 2(a) shows the design of the deposited alignment marks.
Once a wafer has alignment marks, the PM layer is coated by spin coating at 2500 rpm and then drying at 85° C for 1 minute. Four alignment domains need to be registered to one another and therefore an exposure tool with an alignment system is required. Here we use an ABM mask aligner with a 6-axis vacuum stage to perform the exposures. Each exposure generates one quadrant of the macro-pixel. Figure 2(b) shows the alignment mark used for each successive exposure. The majority of the mask is comprised of 7.4 μm boxes that cover every fourth pixel, as shown in Fig. 2(c). The marks require the mask to be indexed by a single pixel (7.4 μm) either vertically or horizontally between exposures. A 4” ultraviolet linear dichroic polarizer manufactured by Boulder Optics, which is placed on top of the chrome mask, is used to define the polarization orientation of each exposure and is changed between each exposure. The exposure time is adjusted for LPUV exposure dose of 80 mJ/cm2 at 365 nm.
After exposure of the PM layer, the wafer is coated with LCP doped with dichroic dye. Dye loading varied between 5 and 20 mg/ml LCP and solvent solution. Coating speeds range from 600 to 3000 rpm. After coating, the LCP is dried for 2 minutes at 55° C. It is important not to exceed 60° C as the LCP has a sharp isotropic phase transition. The dried film is then exposed to unpolarized UV light. Depending on the amount of dye included, a higher or lower intensity is necessary. For 20 mg/ml of dye solution an intensity of 100 mW/cm2 is used. Figure 3(a) shows a micrograph of a set of filter array illuminated with 45° polarized light. A 100x 0.4 NA microscope objective is used to inspect the array for defects and alignment quality. The microscope is not free of diattenuation and therefore the exact transmission is not representative.
The wafer is diced into its respective dies and mounted to a Teflon holder shown in Fig. 3(b). This Teflon package is then used to hold the die during alignment to the CCD. During alignment to the CCD, the sensor is illuminated with polarized light and a 6-axis stage is used to manipulate the Teflon holder relative to the CCD. When the FPA is aligned properly, UV epoxy is applied at the corners of the Teflon holder and is cured to hold the Teflon package in place. Proper alignment to the CCD, especially the residual gap between the CCD and FPA, is extremely important. Effects of improper alignment are discussed in detail in Appendix B.
3. Linear DoFP polarimeter
The first polarimeter assembled is a linear polarimeter with a macro pixel shown in Fig. 3(a). While other patterned LCP polarizers have been demonstrated, this is the first linear DoFP polarimeter constructed with LCP based patterned polarizers. The micropolarizer array is made with a RMS08 LCP solvent solution that is mixed with 10 mg/ml of both purple (G-241) and blue (G-472) dye. Blue and purple dyes were included in equal concentration broad spectrum polarimetric imaging. If the device is to be used for interferometric purposes, optimum dye concentrations can be designed to increase the extinction ratio at specific interferometer wavelengths.
3.1 Bulk polarizer characterization
A 1.5” companion wafer is completed with each 4” wafer. The companion wafer undergoes identical processing except they have a single uniform 0° exposure. These samples are used to estimate the polarization properties of the micropolarizers. Figures 4(a) and 4(b) shows the bulk spectrum and extinction ratio for the device. The solid lines represent measurements from a Varian 5000 UV-VIS-NIR Spectrometer and the circles represent individual measurements using an Axometrics Polarimeter with a variety of 5 nm bandpass filters. Figure 4(c) shows the specific solvent, LCP, and dichroic dye mixture used.
3.2 FPA Mueller matrix images
A Mueller matrix imaging polarimeter (MMIP)  is used to analyze the LCP FPA. The linear diattenuation, linear diattenuation orientation, and depolarization at 600 are shown in Fig. 5 along with cross-section data. The system uses a 40x 0.55 microscope objective and therefore achieving focus is difficult. Proper focus is essential for these measurements because orthogonally polarized light that is recombined is depolarized. Therefore, defocus, scattering, and diffraction all lead to reduction in measured diattenuation and an increase in depolarization. Figure 5 illustrates some high resolution details that can be measured using the MMIP. The diattenuation is uniform in the center of the sample, with low areas at the boundaries between pixels. The diattenuation orientation cross-section alternates between 90° and 135° degree pixels except at the right side where it intersects the boundary of two pixels due to tilt of the sample. The depolarization is roughly 0.15 in the center of the pixels, but increases dramatically at the boundaries due to defocus and undersampling. This level of depolarization will effectively limit the diattenuation of the polarizer to a maximum of 0.85, which is shown in the diattenuation cutline with values centered around 0.77.
3.3 DOLP test
The accuracy of the DOLP estimation was measured by capturing multiple images with varying DOLP. The DOLP was controlled by rotating a nearly quarter-wave retarder in front of a 0° linear polarizer. Due to the change in retardance with wavelength, the spectrum was limited by a 580 nm bandpass filter with a spectral width of 5 nm. Using the Axometrics Mueller Matrix Polarimeter the waveplate was also measured to have a retardance of 98.96°. Figure 6 shows a plot of the average DOLP of the scene with the standard deviation marked by error bars. The average standard deviation for all the measurements was ± 0.053. Thesolid line shows the theoretical DOLP for a horizontal polarization state rotated by an ideal waveplate with a retardance of 98.96°. The four images show a 250x250 crop of the captured images with the fast-axis orientation of the retarder indicated. The noise in the scene is primarily due to pattern defects in the LCP orientations which cannot be easily removed by calibration.
3.4 Sample images
The linear DoFP camera is tested with a few scenes in both indoor and outdoor environments. The test target is a beam chopper with linear polarizers placed in each window. The polarizers in the inside windows are aligned radially and on the outside windows they are aligned tangentially. Figure 7 was taken with a 50 mm lens at f/5.6 with a 0.5 second exposure and ambient fluorescent lighting. The average DOLP in the polarizer regions is 0.783 ± 0.111. Reflections of the surfaces of the polarizers act to reduce the measured DOLP. Particle defects on the FPA are responsible for some defects.
Many natural scenes can have very low polarization signatures, but reflected sky light or high angle reflections produce moderate polarization signatures. Figure 8 shows a parked car on the roof of a parking garage. The sun is near its apex and the windows are reflecting the polarized sky. The metallic siding of the car has a weaker polarization signal, however clearly changes with the shape of siding. The linear angle plot is noisy in low intensity areas as expected, but varies smoothly with changing shape of the body panels. The maximum DOLP of the scene is 0.4.
4. Full Stokes DoFP polarimeter
The second prototype polarimeter is a full Stokes DoFP polarimeter. A primary advantage of LCP based FPAs is that they can be used as retarders or as polarizers when dichroic dye is incorporated. The Full Stokes design here utilizes two layers of patterned LCP material separated by an intermediate buffer layer. Using these two layers, circular or elliptical polarizers can be fabricated, which is not possible using wire-grid polarizer technology. However, spiral plasmonic antennas have recently been shown to function as circular polarizers . A different approach demonstrated recently is to place an electro-active liquid crystal cell in front of a wire-grid polarizer FPA , however multiple time sequential exposures are then necessary.
The macro-pixel design, shown in Fig. 9 , was chosen primarily to demonstrate the fabrication of circular polarizers immediately adjacent to a linear polarizer. As stated above, two layers of LCP material are coated. The first is identical to that described in the linear FPA, except for the orientations of the polarizers. A buffer layer of Norland optical adhesive NOA-81 is then spin coated at 4000 rpm. A second layer of photoalignment material is then coated, cured, and exposed. The second layer of LCP without dichroic dye is then coated at 750 rpm, which results in a thickness with a quarter wave of retardance at 580 nm. The LCP orientations were chosen so that a macro pixel would be comprised of a 0° linear, 45° linear, right-hand circular, and 90° linear polarizers. As shown in Fig. 8, the LCP orientations are 0°-0°, 45°-45°, 0°-45°, and 0°-90° for the retarder and polarizer respectively. When the retarder is at 0° or 90° with respect the polarizer orientation, it is an eigenpolarization of the polarizer and therefore does not affect the transmission. However, at 45° to the polarizer orientation the quarter-wave retarder acts to rotate circularly polarized light to linearly polarized light that will be transmitted or blocked by the polarizer depending on whether right or left handed light is incident.
4.1 FPA Mueller matrix images
The Full Stokes FPAs are also examined using the MMIP. Figure 10 shows the linear and circular diattenuation of the FPA. The linear and circular diattenuation does not reach zero for a circular or linear pixel. This could be due to a variety of issues. Misalignment in the LCP orientations will result in circular diattenuation. For an ideal polarizer and retarder, a 15° angle between axes of the devices results in a circular diattenuation of 0.5. Secondly, deviation from the quarter wave thickness will result in increased linear diattenuation. Scattering in the LCP and barrier layers can possibly cause significant scattering and depolarization. Finally, stress in the barrier material can add random retardance and act as a depolarizer in the optical path.
4.2 DOLP and DOCP test
The accuracy of the DOLP and DOCP estimation is measured by capturing images of varying uniformly polarized light. The ellipticity of the polarization is varied by rotating a nearly quarter-wave retarder in front of a 0° linear polarizer. Due to the change in retardance with wavelength, the spectrum was limited by a 580 nm bandpass filter with a spectral width of 5 nm. Using an Axometrics Mueller Matrix Polarimeter the waveplate was measured to have a retardance of 89.1°. Figure 11 shows a plot of the average DOLP (black) and DOCP (red) of the scene with the standard deviation marked by error bars. The solid lines show the theoretical DOLP and DOCP for a vertical polarization state rotated by an ideal waveplate with a retardance of 89.1°. There is a larger variation in the standard deviation of the measurements to imbalance in the polarization measurements. This will be discussed further on.
4.3 Sample images
The Full-Stokes DoFP prototype camera is tested with a similar target as the linear version. The test target is a beam chopper with linear polarizers oriented tangentially in the outside windows. The inside windows are covered with right–handed circular polarizers. Figure 12 is taken with a 100 mm lens at f/11 with a 5 second exposure and ambient fluorescent lighting that is filtered with a 5 nm bandpass filter centered at 580 nm. The narrow spectral filter is necessary because of the change in retardance with wavelength, which results in the camera calibration being spectrally sensitive. The different polarizer orientations cause large variations in the noise level, particularly for 135° linear or left-handed circular polarization.
While circular polarization is relatively rare in nature, elliptically polarized reflected light from scarab beetles was originally discovered by Michelson in 1911. The beetles have been shown to exhibit both left- and right-handed circular polarization depending on the species. The chirality of the beetles outer structure is responsible for the polarization properties and has previously been examined for many beetles and over a range of incident angles [22, 23]. Figure 13 shows a Plusiotis optima beetle illuminated with diffuse white light. Reflection from the body has a DOCP of roughly 0.4 in the center of the shell. The light reflected off of the sides of the beetle is slightly linearly polarizer due to polarization sensitivity of high angle Fresnel reflections.
5. Future design optimization and conclusions
In this paper, we present a novel method of fabricating a variety of polarization micro-optics and the application of this technology in two prototype DoFP Polarimeters. This technology represents an increase in simplicity and flexibility for the fabrication of micro polarization optics. The most competitive technology, micro wire grid polarizers, requires a process toolset that includes a lithography system capable of printing pitches below 300 nm, an evaporator to deposit metals, and a dry etch system. Comparatively, this process requires only a lithography tool with a resolution better than the pixel size, 7.4 μm in this case. Secondly, the spectral response of the system is only dependent on the dyes incorporated and can therefore be optimized for very narrow or wide spectrums.
The linear DoFP polarimeter represents a basic demonstration of the technology. To the best of our knowledge, our full-Stokes DoFP polarimeter is the first of its kind ever made. The devices shown are still prototypes and improvements in the defect levels and measurement error is necessary. The linear FPA includes four measurements on the equator of the Poincaré Sphere shown in Fig. 14(a) . By moving one of the measurements away from the hemisphere, using a patterned retarder, S3 is measured as well. However, this is an unbalanced design. The area inscribed by the four measurements shown in Fig. 14(b) encompasses only roughly one side of the top hemisphere. The quality and noise level of a polarimeter can be roughly equated to how much area the inscribed measurement points encompass. Optimized polarimeter designs have been studied previously. A patterned polarizer/ and retarder DoFP is equivalent to a spinning retarder division of time polarimeter that records four measurements. Sabatke, et. al.  have shown that the optimized four measurements should form a tetrahedron inscribed in the Poincaré Sphere. For a uniform vertical polarizer and a patterned retarder, the design uses a 135° retarder with fast axis angles of ± 15.1° and ± 51.7°. This could simplify the fabrication and defect density of the FPA as the polarizer can be uniformly aligned. A second option is to pattern both layers and use a 35° retarder, as shown in Fig. 14(c). This allows for a thinner film stack due to the smaller retardance.
Appendix A: Stokes vector estimation and system calibration
An imaging polarimeter indirectly measures Stokes vectors as only intensities can be directly measured. The Stokes vector is inferred by the intensity measurements and a known system configuration. For any system, the output polarization is a function of the input polarization and the system Mueller matrix (M). The system Mueller matrix is the product of the Mueller matrices of the individual elements in the system, which generally consists of some number of diattenuators retarders, and depolarizers. The output polarization, Sout, can be calculated from a known input polarization, Sin, and a system Mueller matrix, Msys, using Eq. (6).
The only value directly measured is the intensity, Sout,0, which can be calculated via Eq. (7).
Note that the intensity is purely dependent on the top row of the Mueller matrix, which is also known as the Analyzer vector (A). Remembering that Sout,0 is the measured value, Sin can be solved for using a system of equations that include at least four unique Analyzer vectors. An array of Analyzer vectors is formed called the Polarimetric Matrix W. I is the measurement vector which is comprised of the Sout,0 measurements.
From Eq. (8) it is clear that by using the pseudo-inverse of W, the input Stokes vector can be calculated, Sin. This is known as the data reduction matrix, W−1.
The dot over Sin indicates that it is an estimated quantity due to noise. The calculation of Sin assumes that W is known, however this is often not the case and W must instead also be determined via system calibration. This is performed via inputting light of a known Stokes vector. An example calculation of W0,0 and W0,1 by inputting 0° and 90° polarized light is shown below.
W0,2 and W0,3 can be similarly calculated by inputting 45° linear, 135° linear, right hand circular, and left handed circular polarization. In this fashion the full polarimetric matrix can be estimated. It is also necessary to account for the spectral dependence of W as the polarization and retardance properties of the elements are a function of wavelength. This can be done by adding spectral filter and calibrating the system over different wavelength bands.
The method described above is for the calibration of a single measurement Stokes polarimeter. An imaging polarimeter collects data over the image field and therefore I, S, and W are functions of position (x,y) and for the case of a CCD they are discrete positions (m,n). Depending on the uniformity of the optical elements over the field, an average W matrix can be used or it can be calculated for each sample point. It was assumed that array defects, coating uniformity, and error in FPA alignment would cause changes in our W matrix over the extent of the CCD and therefore an individual W matrix is calculated for each pixel. This was performed by capturing a series of 40 images while the CCD was illuminated with uniform white linearly polarizer light. For the linear DoFP, a 500 nm long pass filter is installed in front of the CCD in order to limit the spectrum to the wavelengths the dyes are most sensitive to. Four linear polarization orientations, 0°, 45°, 90°, and 135°, were used and ten images were acquired at each orientation. The ten images were then averaged to produce four master calibration images. These images were used to calculate the Analyzer vectors for each pixel as described in Eqs. (10)–(13). A collection of four neighboring pixels, (n,m), (n+1,m),(n,m+1), and (n+1,m+1), are then used to calculate the individual W and W−1 matrices. More sophisticated calibration, interpolation , and deconvolution techniques  can also be applied to improve data quality and resolution.
Linear operation of the detector is also of importance. Ideally, the detector is treated as linear and without a polarization specific response, however all CCD and CMOS sensors have a linear and non-linear regimes and therefore it is important to only operate them in the linear regime or by properly characterizing their nonlinear response.
Appendix B: Effects of focal plane array gap and lens f-number on image quality
A critically important step in the fabrication is the bonding of the FPA to the CCD. The FPA needs to be aligned to the CCD in all three spatial dimensions as well as two tilt axis. This operation was performed for us by 4D Technology located in Tucson AZ.
Errors arise from significant spacing between the FPA and the CCD which are related to both the focal length and f-number of the system. This is the case for the very first prototype camera constructed. Figure 15 shows how the spacing between the FPA and the CCD causes a vertical offset between where the chief ray strikes the FPA and CCD. As the offset increases radially away from the optical axis, the Stokes values and DOLP fall to zero as averaging occurs between neighboring pixels. When the magnitude of the offset reaches a full pixel height, 7.4 μm for this CCD, the measured Stokes value is equal to the negative of its original value. At an offset of 1.5 pixels the Stokes values again fall to zero before rising back to their original value. This cycle repeats continuously with an offset period equal to the height of two pixels. The Stokes images in Fig. 15 were generated from imaging a scene of uniform horizontally polarized light using an earlier prototype linear DoFP polarimeter. As expected, the pitch of the pattern roughly doubles in size between the 50mm and 100mm focal length lenses. Interestingly, the gap between the FPA and CCD can be estimated from the resulting images. Each complete period of the pattern is the equivalent of two pixels of vertical offset, which is 14.8 μm. From the geometry of similar triangles in Fig. 15 and knowing the total number of periods, number of pixels in the image, and the lens focal length the gap is estimated to be 76 μm.
Performance degradation also occurs with decreasing f-number. As the f-number increases the marginal ray angle increases and the diameter of the image-space cone of light at the FPA can exceed the size of an individual pixel. Figure 16 shows a diagram illustrating an imaging configuration with three different f-numbers. The high f-number has no averaging and therefore measures the full range of the Stokes parameter, an example of which is shown by the f/22 image. As the f-number decreases, averaging with areas outside of the intended FPA pixel occurs and results in a reduced effective extinction ratio and therefore a lower measured Stokes value and DOLP. The f/16 image shows this as the maximum value of S1 and S2 is ±0.5. If the f-number is further decreased, the effective polarization orientation changes because a larger area of the orthogonal orientation is included in the average. In the f/11 image, the sign of the Stokes values is flipped and the maximum value is now ±0.2.
The polarimeters described in sections 3 and 4 have a much smaller gap than the earlier prototype that is used to capture the images in Figs. 15 and 16. However, the devices still show significant degradation in performance at low f-numbers. Figure 17 shows a plot of extinction ratio versus f-number for the linear DoFP polarimeter from section 3 using three different focal length lenses. The extinction ratio was measured by dividing each image into its sub-pixels components, resulting in four images with a quarter of the resolution. On a per pixel basis, the 0° image was divided by the 90° image, which yielded a pixel level map of the extinction ratio. The mean and standard deviation of the scene is then calculated. There is slight reduction in peak extinction ratio between the 50 and 100 mm lens, but at equivalent f-numbers the values are within one standard deviation between the 100 and 500 mm lenses. For all the lenses, significant roll off in extinction ratio occurs at f-numbers below 8. The residual gap and the one micron thickness of the film still affect the performance at low f-numbers and short focal lengths. This reinforces the importance of reducing the overall thickness of the devices and any gap between the FPA and the filters, which will be critically necessary in improving future devices.
This work is funded by the United States Air Force Office of Scientific Research (AFOSR) Multi-University Research Initiative (MURI) Program under Award FA9550-09-1-0669-DOD35CAP and by the Arizona Technology Research Infrastructure Fund (TRIF). The authors thank Prof. Thomas Milster’s, Prof. Scott Tyo, and Prof. Nasser Peyghambarian’s research groups for allowing us to utilize their equipments and for donating their time. The authors would also like to thank Dainippon Ink and Chemical for material donations and Prof. Peter Vukusic for providing us samples of the beetle.
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